The problem of Orthogonality: gives $n$ vectors of dimension $k$ and another set of same, can a pair be found with inner product = $0$?
The problem of max product: likewise two sets each $n$ vectors (I forgot to mention in both cases values are binary). We want to find maximal inner product (one vector from set $A$ and one from $B$).
I want to find a reduction between OV to max. Inner product.
My idea: Use negative values, claim its equivalent with negative value and possitive values.
What I mean, OV reduced to max. Inner prod with negative values by multiplying all by $-1$.
Then if maximum is zero... Orthogonality. Else, no orthogonality.
But i need to argue negative max inner product equivalent to max. Inner product.
Maybe there is another way?
If it does not work, also interested in reduction from sat.